Answer
(a). $n(t)=29.76e^{0.013t}$
(b).$t=53.32$
(c). $n(10)=29.76e^{0.013\times10}=33.8$
Accrording to the US census bureu, The population of california in 2010 is $37.32$
Work Step by Step
$n(t)=n_0\times e^{rt}$. Whereas,$n(t)$ is population at time $t$, $n_0$ is Initial size of the population, $r$ is relative rate of growth, and $t$ is time.
(a). $n_0=29.76$, $n(10)=33.87$,
$n(10)=29.76e^{10r}=33.87$,
$e^{10r}=1.14$,
$10r=\ln 1.14$,
$r=0.013$.
Therefore, $n(t)=29.76e^{0.013t}$
(b). $n_0 \times2=59.52$
$n(t)=29.76e^{0.013t}=59.52$
$e^{0.013t}=2$,
$0.013t=\ln 2$,
$t=53.32$
(c). $n(10)=29.76e^{0.013\times10}=33.8$
Accrording to the US census bureu, The population of california in 2010 is $37.32$
